10 guage is too small for a 350w rms 600 peak sub setup right?

Well, that depends. If you are mounting the amp only a few feet from the battery, then it would be fine. If you are putting it under a seat or in the trunk like most people, then the answer is no. A wire's current carrying ability decreases as the wire gets longer.

Also, you forgot to mentino the particular amp. Even if they are rated for the same output, every amp has a different current demand.

Assuming it's a typical class a/b amp that isn't too tightly regulated, I would run 4 ga. This is overkill for a typical 350W sub amp, but it gives you room to upgrade in the future. You probably could run 8 ga as well. Sure its more expensive for the 4 ga now, but when you decide to add another amp, then you have to rip out the old stuff and put down 4 ga. Also, you don't want your car to turn into a ball of flames because you cheaped out on a few dollars of power wire!

I don't know about the "ball of flames" statement. Unless the car audio gods unleash their wrath upon this young lad for using a slightly smaller wire than you think he should use.

10 gauge will work fine, as long as you use a grommet in the firewall, or run it through a protected area. I would use 8 gauge at the least for any sub amp install, but... if that's all you have to work with don't worry. Just try to run the power wires on the opposite side of the car to protect the signal wires; i.e. speaker cable, RCA, etc. from interference.

One of my friends power wire went up in flames. Cooked up really fast too

haha, you reminded me of a time too. friend of mine screwed his plastic door jam back on, right through the wire. I didnt know he did it that way and we are sitting in his car waiting for someone and POOF!! smoke starts billowing out from his door. he freaked out and jumped out of the car so fast. It had to be one of the funniest things ive ever seen.